Question: Luiza is jumping on a trampoline. $H(t)$ models her distance above the ground (in $\text{m}$ ) $t$ seconds after she starts jumping. Here, $t$ is entered in radians. $H(t) = -0.6\cos\left(\dfrac{2\pi}{2.5}t\right) + 1.5$ What is the second time when Luiza reaches a height of $1.2\text{ m}$ ? Round your final answer to the nearest hundredth of a second.
Converting the problem into mathematical terms $H(t) = -0.6\cos\left({\dfrac{2\pi}{2.5}}t\right) + 1.5$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{2.5}}}=2.5$ seconds. We want to find the second solution to the equation $H(t)=1.2$ within the period $0<t<2.5$. The answer The equation's two solutions within the desired period (rounded to the nearest hundredth of a second) are $0.42$ and $2.08$. Therefore, Luiza reaches a height of $1.2\text{ m}$ for the second time $2.08$ seconds after she starts jumping.